Statistics 7.1-7.2: Large-Sample Confidence Interval for a Population Mean (μ)

Target parameter

the unknown population parameter that we are interested in estimating

Point estimator

singles number to estimate the population parameter

Confidence Interval

is a formula that tells us how to use sample data to calculate an interval that estimates a population

Confidence Coefficient

is the probability that a randomly selected confidence interval encloses the population parameter

Confidence Level

is the confidence coefficient expressed as a percentage

Required Conditions

1. A random sample is selected from the population (no bias)

2. σ is known and the sample size is large (σ is unknown —> use s)

Interpretation

“In repeated sampling, we are 100(1-α)% confident that the true population mean (μ) lies somewhere between …. and ….”

“We can say this because we know that if we were to repeat the study many, many times, and compute confidence intervals in the same way, about 100(1-α)% of the intervals would include the population mean (μ)